Question

If $f(x) = 3x + 5$ and $g(x) = x^2 - 1,$ then (fog) $(x^2 - 1)$ is equal to

• A. $3x^4 - 3x + 5$
• B. $3x^4 - 6x^2 + 5$
• C. $6x^4 + 3x^2 + 5$
• D. $6x^4 - 6^x + 5$
• E. $3x^2 + 6^x + 4$

Answer 1

Answer: (B)

$\because f(x)=3 x+5$
and $g(x)=x^{2}-1$
$\therefore $ fog $\left(x^{2}-1\right) =f\left[g\left(x^{2}-1\right)\right]$
$=f\left[\left(x^{2}-1\right)^{2}-1\right]$
$=f\left[x^{4}-2 x^{2}+1-1\right]=f\left[x^{4}-2 x^{2}\right]$
$=3\left(x^{4}-2 x^{2}\right)+5$
$=3 x^{4}-6 x^{2}+5$